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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)



The role of the Ramanujan conjecture in analytic number theory

Authors: Valentin Blomer and Farrell Brumley
Journal: Bull. Amer. Math. Soc. 50 (2013), 267-320
MSC (2010): Primary 11F70
Published electronically: January 14, 2013
MathSciNet review: 3020828
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Abstract: We discuss progress towards the Ramanujan conjecture for the group $ \mathrm {GL}_n$ and its relation to various other topics in analytic number theory.

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Additional Information

Valentin Blomer
Affiliation: Mathematisches Institut, Bunsenstr. 3-5, 37073 Göttingen

Farrell Brumley
Affiliation: Institut Galilée, Université Paris 13, 99 avenue J.-B. Clément, 93430 Villetaneuse, France

Keywords: Ramanujan conjecture, $L$-functions, number fields, non-vanishing, functoriality
Received by editor(s): June 8, 2012
Published electronically: January 14, 2013
Additional Notes: The first author was supported by the Volkswagen Foundation and a Starting Grant of the European Research Council. The second author is partially supported by the ANR grant ArShiFo ANR-BLANC-114-2010 and by the Advanced Research Grant 228304 from the European Research Council.
Dedicated: Dedicated to the 125th birthday of Srinivasa Ramanujan
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.